Testing with Limited Capacity and Pooling

Motivated by the persistent lack of testing capacity in the COVID-19 pandemic, we study the question “who should be tested?” when capacity is limited, tests have errors, and patients differ in their prior probability of being infected. While health officials initially prioritized testing patients who were highly likely to be infected, we find that it may be better to focus on patients who are less likely to be infected, particularly when the false-negative rate is substantial. We also consider pooled testing, a method of grouping samples to conserve tests. When pooled testing is an option, it may be optimal to test two groups of individuals: those who are very likely to be infected and those who are very unlikely to be infected. Moreover, even though pooling is an option, it can still be optimal to reserve some individual tests for samples from patients for whom the outcome is most uncertain. The results apply to any situation where testing capacity is inadequate to test the number of potentially infected individuals, and they can inform both public health policy and healthcare operations management.